Decomposability of finitely presented modules
Author:
R. B. Warfield
Journal:
Proc. Amer. Math. Soc. 25 (1970), 167-172
MSC:
Primary 13.40
DOI:
https://doi.org/10.1090/S0002-9939-1970-0254030-4
MathSciNet review:
0254030
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Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that a commutative ring with $1$ has the property that every finitely presented module is a summand of a direct sum of cyclic modules if and only if it is locally a generalized valuation ring. A Noetherian ring has this property if and only if it is a direct product of a finite number of Dedekind domains and an Artinian principal ideal ring. Any commutative local ring which is not a generalized valuation ring has finitely presented indecomposable modules requiring arbitrarily large numbers of generators.
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Keywords:
Indecomposable modules,
generalized valuation rings,
direct sums of cyclic modules
Article copyright:
© Copyright 1970
American Mathematical Society